We study the state complexity of a class of simple languages. If A is an alphabet of k letters, a k-language is a nonempty set of words of length k, that is, a uniform language of length k. By a new construction, we show that the maximal state complexity of a k-language is (k − 1)/(k − 1) + 2 + 1, and every k-language of this complexity is also a uniform language of length k of the maximal stat...

The paper concerns minimal nonconstructible blocks of cellular automata, i.e. minimal combinations of cell states that never appear in the evolution of an automaton. Using our previous work on the construction of predecessors of given configurations, we analyze with numerical experiments the sets of nonconstructible blocks for 1D cellular automata with binary and ternary neighbourhoods and bina...

A prominent learning algorithm is Angluin’s L∗ algorithm, which allows to learn a minimal deterministic automaton using so-called membership and equivalence queries addressed to a teacher. In many applications, however, a teacher might be unable to answer some of the membership queries because parts of the object to learn are not completely specified, not observable, it is too expensive to reso...

Multirobot systems (MRSs) are capable of solving task complexity, increasing performance in terms of maximizing spatial/ temporal/radio coverage or minimizing mission completion time. They are also more reliable than single-robot systems as robustness is increased through redundancy. Many applications such as rescue, reconnaissance, and surveillance and communication relaying require the MRS to...

Abstract We show the decidability of finite sequentiality problem for unambiguous max-plus tree automata. A automaton is called if there at most one accepting run on every tree. The asks whether a given automaton, exist finitely many deterministic automata whose pointwise maximum equivalent to automaton.

A significant result in the structure theory of regular languages is the Krohn-Rhodes Theorem, which states that any finite automaton can be decomposed into simple “prime factors”. This theorem can be stated in different versions using different products on different structures, namely the cascade product of automata, the wreath product of transformation semigroups and the block product of semi...

A language L is prefix-closed if w ∈ L implies that every prefix of w is in L. It is known that a regular language is prefix-closed if and only if it is accepted by a nondeterministic finite automaton (NFA) with all states final [18]. In the minimal incomplete deterministic finite automaton (DFA) for a prefix-closed language, all the states are final as well. The authors of [18] examined severa...

The ‘minimal’ payment—a payment method which minimizes the number of coins in a purse—is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. The delay plot shows visually that the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the averag...

The 1984 article by Martin, Odlyzko and Wolfram on Wolfram’s Rule 90 heightened interest in the area of linear cellular automata defined on a vector space over a finite field [8]. In this article we find the closed form expression for the minimal polynomial of Rule 90, which is then used to completely characterize the dynamics of the map. In addition, we show that the standard basis vectors in ...

Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers β and γ respectively, such that β and γ are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of...